The understanding of Particle Physics have been challenged and improved by the recent experimental results obtained by the LHC, the Pierre
Auger and IceCube Neutrino Observatories [1]}. In particular, in
recent years, IceCube measured the astrophysical and atmospheric
neutrinos fluxes at high energies
[2]}, [3]}, [4]} and different collaborations
from the LHC performed several analyses of the heavy meson production at
high energies and forward rapidities
[5]}, [6]}, [7]}, [8]}.
Such distinct sets of data are intrinsically related, since the
description of the heavy meson production
at the LHC and higher center of mass energies is fundamental to make
predictions of the prompt neutrino flux [9]}, which
is expected to dominate the atmospheric \(\nu \)  flux for large neutrino energies
[10]}. An important question,
which motivate the present study, is whether the current and future
IceCube data can shed light on charm production at the LHC and vice -
versa and in particular on the intrinsic charm in the nucleon.
